Question

A cylinder with height 10 inches and radius 4 inches is filled with water. The water is poured into a bowl

(hemisphere) with radius 5 inches. Sketch a cylinder and a hemisphere with dimensions labeled. If all the water
will fit, tell how much empty space remains in the bowl. If all the water will not fit, tell how much water is left in
the cylinder. (leave your answer in terms of pi)

Answer 1

Volume of water left in the cylinder=
`76(2)/(3)\pi \:in^3`

Explanation:

Height of the Cylinder=10 inches

Radius of the cylinder=4 Inches

Volume of the Cylinder

`=\pi r^2h\\=4^2*10\pi\\=160\pi\:in^3`

Radius of the Hemisphere=5 Inches

`\text{Volume of a Hemisphere}=(2)/(3)\pi r^3\\ =(2)/(3)\pi *5^3\\=(250\pi)/(3) in^3`

Since the Volume of the cylinder is greater than the Volume of the bowl, all the water will not fit.

`\text{Therefore: volume of water left} =160\pi-(250\pi)/(3)\\=76(2)/(3)\pi \:in^3`